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A049381 Expansion of (1-25*x)^(-3/5).

%I A049381 #22 Sep 24 2023 09:15:35
%S A049381 1,15,300,6500,146250,3363750,78487500,1850062500,43938984375,
%T A049381 1049653515625,25191684375000,606890578125000,14666522304687500,
%U A049381 355381117382812500,8630684279296875000,210013317462890625000
%N A049381 Expansion of (1-25*x)^(-3/5).
%H A049381 Robert Israel, <a href="/A049381/b049381.txt">Table of n, a(n) for n = 0..715</a>
%F A049381 G.f.: (1-25*x)^(-3/5).
%F A049381 a(n) = (5^n/n!) * Product_{k=0..n-1} (5*k+3).
%F A049381 a(n) ~ Gamma(3/5)^-1*n^(-2/5)*5^(2*n)*{1 - 3/25*n^-1 + ...}. - Joe Keane (jgk(AT)jgk.org), Nov 24 2001
%F A049381 a(n) = (-25)^n*binomial(-3/5, n). - _Peter Luschny_, Oct 23 2018
%F A049381 From _Peter Bala_, Sep 24 2023: (Start)
%F A049381 a(n) = 25^n * binomial(n - 2/5, n).
%F A049381 P-recursive: a(n) = 5*(5*n - 2)/n * a(n-1) with a(0) = 1. (End)
%e A049381 (1-x)^(-3/5) = 1 + 3/5*x + 12/25*x^2 + 52/125*x^3 + ...
%p A049381 A049381 := n -> (-25)^n*binomial(-3/5, n):
%p A049381 seq(A049381(n), n=0..16); # _Peter Luschny_, Oct 23 2018
%t A049381 CoefficientList[Series[(1-25x)^(-3/5),{x,0,20}],x] (* _Harvey P. Dale_, Aug 08 2013 *)
%Y A049381 Cf. A034688, A049380, A049382, A049392, A049396.
%K A049381 nonn,easy
%O A049381 0,2
%A A049381 Joe Keane (jgk(AT)jgk.org)